// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
//
// This code initially comes from MINPACK whose original authors are:
// Copyright Jorge More - Argonne National Laboratory
// Copyright Burt Garbow - Argonne National Laboratory
// Copyright Ken Hillstrom - Argonne National Laboratory
//
// This Source Code Form is subject to the terms of the Minpack license
// (a BSD-like license) described in the campaigned CopyrightMINPACK.txt file.

#ifndef EIGEN_LMONESTEP_H
#define EIGEN_LMONESTEP_H

namespace Eigen {

template<typename FunctorType>
LevenbergMarquardtSpace::Status
LevenbergMarquardt<FunctorType>::minimizeOneStep(FVectorType& x)
{
	using std::abs;
	using std::sqrt;
	RealScalar temp, temp1, temp2;
	RealScalar ratio;
	RealScalar pnorm, xnorm, fnorm1, actred, dirder, prered;
	eigen_assert(x.size() == n); // check the caller is not cheating us

	temp = 0.0;
	xnorm = 0.0;
	/* calculate the jacobian matrix. */
	Index df_ret = m_functor.df(x, m_fjac);
	if (df_ret < 0)
		return LevenbergMarquardtSpace::UserAsked;
	if (df_ret > 0)
		// numerical diff, we evaluated the function df_ret times
		m_nfev += df_ret;
	else
		m_njev++;

	/* compute the qr factorization of the jacobian. */
	for (int j = 0; j < x.size(); ++j)
		m_wa2(j) = m_fjac.col(j).blueNorm();
	QRSolver qrfac(m_fjac);
	if (qrfac.info() != Success) {
		m_info = NumericalIssue;
		return LevenbergMarquardtSpace::ImproperInputParameters;
	}
	// Make a copy of the first factor with the associated permutation
	m_rfactor = qrfac.matrixR();
	m_permutation = (qrfac.colsPermutation());

	/* on the first iteration and if external scaling is not used, scale according */
	/* to the norms of the columns of the initial jacobian. */
	if (m_iter == 1) {
		if (!m_useExternalScaling)
			for (Index j = 0; j < n; ++j)
				m_diag[j] = (m_wa2[j] == 0.) ? 1. : m_wa2[j];

		/* on the first iteration, calculate the norm of the scaled x */
		/* and initialize the step bound m_delta. */
		xnorm = m_diag.cwiseProduct(x).stableNorm();
		m_delta = m_factor * xnorm;
		if (m_delta == 0.)
			m_delta = m_factor;
	}

	/* form (q transpose)*m_fvec and store the first n components in */
	/* m_qtf. */
	m_wa4 = m_fvec;
	m_wa4 = qrfac.matrixQ().adjoint() * m_fvec;
	m_qtf = m_wa4.head(n);

	/* compute the norm of the scaled gradient. */
	m_gnorm = 0.;
	if (m_fnorm != 0.)
		for (Index j = 0; j < n; ++j)
			if (m_wa2[m_permutation.indices()[j]] != 0.)
				m_gnorm = (std::max)(m_gnorm,
									 abs(m_rfactor.col(j).head(j + 1).dot(m_qtf.head(j + 1) / m_fnorm) /
										 m_wa2[m_permutation.indices()[j]]));

	/* test for convergence of the gradient norm. */
	if (m_gnorm <= m_gtol) {
		m_info = Success;
		return LevenbergMarquardtSpace::CosinusTooSmall;
	}

	/* rescale if necessary. */
	if (!m_useExternalScaling)
		m_diag = m_diag.cwiseMax(m_wa2);

	do {
		/* determine the levenberg-marquardt parameter. */
		internal::lmpar2(qrfac, m_diag, m_qtf, m_delta, m_par, m_wa1);

		/* store the direction p and x + p. calculate the norm of p. */
		m_wa1 = -m_wa1;
		m_wa2 = x + m_wa1;
		pnorm = m_diag.cwiseProduct(m_wa1).stableNorm();

		/* on the first iteration, adjust the initial step bound. */
		if (m_iter == 1)
			m_delta = (std::min)(m_delta, pnorm);

		/* evaluate the function at x + p and calculate its norm. */
		if (m_functor(m_wa2, m_wa4) < 0)
			return LevenbergMarquardtSpace::UserAsked;
		++m_nfev;
		fnorm1 = m_wa4.stableNorm();

		/* compute the scaled actual reduction. */
		actred = -1.;
		if (Scalar(.1) * fnorm1 < m_fnorm)
			actred = 1. - numext::abs2(fnorm1 / m_fnorm);

		/* compute the scaled predicted reduction and */
		/* the scaled directional derivative. */
		m_wa3 = m_rfactor.template triangularView<Upper>() * (m_permutation.inverse() * m_wa1);
		temp1 = numext::abs2(m_wa3.stableNorm() / m_fnorm);
		temp2 = numext::abs2(sqrt(m_par) * pnorm / m_fnorm);
		prered = temp1 + temp2 / Scalar(.5);
		dirder = -(temp1 + temp2);

		/* compute the ratio of the actual to the predicted */
		/* reduction. */
		ratio = 0.;
		if (prered != 0.)
			ratio = actred / prered;

		/* update the step bound. */
		if (ratio <= Scalar(.25)) {
			if (actred >= 0.)
				temp = RealScalar(.5);
			if (actred < 0.)
				temp = RealScalar(.5) * dirder / (dirder + RealScalar(.5) * actred);
			if (RealScalar(.1) * fnorm1 >= m_fnorm || temp < RealScalar(.1))
				temp = Scalar(.1);
			/* Computing MIN */
			m_delta = temp * (std::min)(m_delta, pnorm / RealScalar(.1));
			m_par /= temp;
		} else if (!(m_par != 0. && ratio < RealScalar(.75))) {
			m_delta = pnorm / RealScalar(.5);
			m_par = RealScalar(.5) * m_par;
		}

		/* test for successful iteration. */
		if (ratio >= RealScalar(1e-4)) {
			/* successful iteration. update x, m_fvec, and their norms. */
			x = m_wa2;
			m_wa2 = m_diag.cwiseProduct(x);
			m_fvec = m_wa4;
			xnorm = m_wa2.stableNorm();
			m_fnorm = fnorm1;
			++m_iter;
		}

		/* tests for convergence. */
		if (abs(actred) <= m_ftol && prered <= m_ftol && Scalar(.5) * ratio <= 1. && m_delta <= m_xtol * xnorm) {
			m_info = Success;
			return LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall;
		}
		if (abs(actred) <= m_ftol && prered <= m_ftol && Scalar(.5) * ratio <= 1.) {
			m_info = Success;
			return LevenbergMarquardtSpace::RelativeReductionTooSmall;
		}
		if (m_delta <= m_xtol * xnorm) {
			m_info = Success;
			return LevenbergMarquardtSpace::RelativeErrorTooSmall;
		}

		/* tests for termination and stringent tolerances. */
		if (m_nfev >= m_maxfev) {
			m_info = NoConvergence;
			return LevenbergMarquardtSpace::TooManyFunctionEvaluation;
		}
		if (abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() &&
			Scalar(.5) * ratio <= 1.) {
			m_info = Success;
			return LevenbergMarquardtSpace::FtolTooSmall;
		}
		if (m_delta <= NumTraits<Scalar>::epsilon() * xnorm) {
			m_info = Success;
			return LevenbergMarquardtSpace::XtolTooSmall;
		}
		if (m_gnorm <= NumTraits<Scalar>::epsilon()) {
			m_info = Success;
			return LevenbergMarquardtSpace::GtolTooSmall;
		}

	} while (ratio < Scalar(1e-4));

	return LevenbergMarquardtSpace::Running;
}

} // end namespace Eigen

#endif // EIGEN_LMONESTEP_H
